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Volumn 20, Issue 1, 2000, Pages 153-166

Dissipativity of Runge-Kutta methods for dynamical systems with delays

Author keywords

Delays; Dissipativity; Dynamical systems; Runge kutta methods

Indexed keywords

DYNAMICAL SYSTEMS; INITIAL VALUE PROBLEMS; NUMERICAL METHODS;

EID: 0034348784     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/20.1.153     Document Type: Article
Times cited : (57)

References (28)
  • 1
    • 0016463497 scopus 로고
    • Special stability problems for functional equations
    • BARWELL, V. K. 1975 Special stability problems for functional equations. BIT, 130-135.
    • (1975) BIT , pp. 130-135
    • Barwell, V.K.1
  • 2
    • 38249014185 scopus 로고
    • Strong contractivity properties of numerical methods for ordinary and delay differential equations
    • BELLEN, A. & ZENNARO, M. 1992 Strong contractivity properties of numerical methods for ordinary and delay differential equations. Appl. Numer. Math. 9, 321-346.
    • (1992) Appl. Numer. Math. , vol.9 , pp. 321-346
    • Bellen, A.1    Zennaro, M.2
  • 3
    • 34250227840 scopus 로고
    • P-stable and P[α, β]-stable integration/interpolation methods in the solution of retarded differential-difference equations
    • BICKART, T. A. 1982 P-stable and P[α, β]-stable integration/interpolation methods in the solution of retarded differential-difference equations. BIT 22, 464-416.
    • (1982) BIT , vol.22 , pp. 464-1416
    • Bickart, T.A.1
  • 4
    • 0002351173 scopus 로고
    • Stability criteria for implicit Runge-Kutta methods
    • BURRAGE, K. & BUTCHER, J. C. 1979 Stability criteria for implicit Runge-Kutta methods. SIAM J. Numer. Anal. 16, 46-57.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 46-57
    • Burrage, K.1    Butcher, J.C.2
  • 5
    • 0001356367 scopus 로고
    • Non-linear stability of a general class of differential equation methods
    • BURRAGE, K. & BUTCHER, J. C. 1980 Non-linear stability of a general class of differential equation methods. BIT 20, 185-203.
    • (1980) BIT , vol.20 , pp. 185-203
    • Burrage, K.1    Butcher, J.C.2
  • 6
    • 0016647175 scopus 로고
    • A stability property of implicit Runge-Kutta methods
    • BUTCHER, J. C. 1975 A stability property of implicit Runge-Kutta methods. BIT 15, 358-361.
    • (1975) BIT , vol.15 , pp. 358-361
    • Butcher, J.C.1
  • 7
    • 0002240895 scopus 로고
    • A generalization of algebraic stability for Runge-Kutta methods
    • COOPER, G. J. 1984 A generalization of algebraic stability for Runge-Kutta methods. IMA J. Numer. Anal. 4, 421-440.
    • (1984) IMA J. Numer. Anal. , vol.4 , pp. 421-440
    • Cooper, G.J.1
  • 8
    • 0002089844 scopus 로고
    • Sur la B-stabilite des methodes de Runge-Kutta
    • CROUZEIX, M. 1979 Sur la B-stabilite des methodes de Runge-Kutta. Numer. Math. 32, 75-82.
    • (1979) Numer. Math. , vol.32 , pp. 75-82
    • Crouzeix, M.1
  • 9
    • 11044230975 scopus 로고
    • A special stability problem for linear multistep methods
    • DAHLQUIST, G. 1963 A special stability problem for linear multistep methods. BIT 3, 27-43.
    • (1963) BIT , vol.3 , pp. 27-43
    • Dahlquist, G.1
  • 11
    • 0000005117 scopus 로고
    • G-stability is equivalent to A-stability
    • DAHLQUIST, G. 1978 G-stability is equivalent to A-stability. BIT 18, 384-401.
    • (1978) BIT , vol.18 , pp. 384-401
    • Dahlquist, G.1
  • 12
    • 0002152673 scopus 로고
    • Generalized disks of contractivity for explicit and implicit Runge-Kutta methods
    • DAHLQUIST, G. & JELTSCH, R. 1979 Generalized disks of contractivity for explicit and implicit Runge-Kutta methods. TRITA-NA Report 7906.
    • (1979) TRITA-NA Report 7906
    • Dahlquist, G.1    Jeltsch, R.2
  • 16
    • 0000614713 scopus 로고    scopus 로고
    • Global dissipativity for A-stable methods
    • HILL, A. T. 1997a Global dissipativity for A-stable methods. SIAM J. Numer. Anal. 34, 119-142.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 119-142
    • Hill, A.T.1
  • 17
    • 0002548250 scopus 로고    scopus 로고
    • Dissipativity of Runge-Kutta methods in Hilbert spaces
    • HILL, A. T. 1997b Dissipativity of Runge-Kutta methods in Hilbert spaces. BIT 37, 37-42.
    • (1997) BIT , vol.37 , pp. 37-42
    • Hill, A.T.1
  • 18
    • 0001129731 scopus 로고    scopus 로고
    • Stability analysis of Runge-Kutta methods for non-linear delay differential equations
    • HUANG, C., FU, H., LI, S., & CHEN, G. 1999a Stability analysis of Runge-Kutta methods for non-linear delay differential equations. BIT 39, 270-280.
    • (1999) BIT , vol.39 , pp. 270-280
    • Huang, C.1    Fu, H.2    Li, S.3    Chen, G.4
  • 19
    • 0033097062 scopus 로고    scopus 로고
    • Stability and error analysis of one-leg methods for nonlinear delay differential equations
    • HUANG, C., LI, S., FU, H., & CHEN, G. 1999b Stability and error analysis of one-leg methods for nonlinear delay differential equations. J. Comput. Appl. Math. 103, 263-279.
    • (1999) J. Comput. Appl. Math. , vol.103 , pp. 263-279
    • Huang, C.1    Li, S.2    Fu, H.3    Chen, G.4
  • 20
    • 0028517853 scopus 로고
    • Runge-Kutta methods for dissipative and gradient dynamical systems
    • HUMPHRIES, A. R. & STUART, A. M. 1994 Runge-Kutta methods for dissipative and gradient dynamical systems. SIAM J. Numer. Anal. 31, 1452-1485.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1452-1485
    • Humphries, A.R.1    Stuart, A.M.2
  • 21
    • 34249839190 scopus 로고
    • A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
    • IN'T HOUT, K. J. 1992 A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations. BIT 32, 634-649.
    • (1992) BIT , vol.32 , pp. 634-649
    • In't Hout, K.J.1
  • 22
    • 0001372973 scopus 로고    scopus 로고
    • A note on unconditional maximum norm contractivity of diagonally split Runge-Kutta methods
    • IN'T HOUT, K. J. 1996 A note on unconditional maximum norm contractivity of diagonally split Runge-Kutta methods. SIAM J. Numer. Anal. 33, 1125-1134.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1125-1134
    • In't Hout, K.J.1
  • 25
    • 38249024166 scopus 로고
    • Stability of numerical methods for delay defferential equations
    • TORELLI, L. 1989 Stability of numerical methods for delay defferential equations. J. Comput. Appl. Math. 25, 15-26.
    • (1989) J. Comput. Appl. Math. , vol.25 , pp. 15-26
    • Torelli, L.1
  • 26
    • 0022016198 scopus 로고
    • The stability of difference formulas for delay differential equations
    • WATANABE, D. S. & ROTH, M. G. 1985 The stability of difference formulas for delay differential equations. SIAM J. Numer. Anal. 22, 132-145.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 132-145
    • Watanabe, D.S.1    Roth, M.G.2
  • 27
    • 0000750163 scopus 로고
    • P-stability of Runge-Kutta methods for delay differential equations
    • ZENNARO, M. 1986 P-stability of Runge-Kutta methods for delay differential equations. Numer. Math. 49, 305-318.
    • (1986) Numer. Math. , vol.49 , pp. 305-318
    • Zennaro, M.1
  • 28
    • 38249006326 scopus 로고
    • Contractivity of Runge-Kutta methods with respect to forcing terms
    • ZENNARO, M. 1993 Contractivity of Runge-Kutta methods with respect to forcing terms. Appl. Numer. Math. 10, 321-345.
    • (1993) Appl. Numer. Math. , vol.10 , pp. 321-345
    • Zennaro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.